Problem

Solve each problem. Repeat Exercise 41 , but assu…

02:44

Problem 41 Hard Difficulty

Solve each problem.
Nancy Bondy's aunt has promised to deposit $\$ 1$ in her account on the first day of her birthday month, $\$ 2$ on the second day, $\$ 3$ on the third day, and so on for 30 days. How much will this amount to over the entire month?

Answer

$\$ 465$

Related Courses

Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 2

Arithmetic Sequences

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Video Transcript

So in this problem, we're told that this girl's aunt is going to put a dollar in her account on the first day of her birthday month, $2 on the second day, three days on the third day. And she's gonna continue this for the whole month, which apparently has 30 days. We're trying to figure out the total that the eye has deposited at the end of the month. So because we're trying to find the total, that means we're trying to find s event. So let's think about the information we know. Let's think of it as a sequence. So she puts $1. The first day chewed the second three, the 1st, 3rd and so forth. We kind of have our medic sequence here, so we know a sub one A. Someone is how much is deposited the first day, which is one now, because she's increasing her amount by one each day. That means our common difference is also one, and this is gonna happen for 30 days. That's good to represent our end, though you so n is equal to 30. So because we have a serve one d and end, we're gonna use the second of our summation formulas, which, if you recall, is Esa Ben is equal to end over two times the quantity of two times a someone plus and minus one times d. So now we're just going to substitute these values into our formula. So we have s of 30 equals 30 divided by two times, two times one plus 30 minus one times one. So now, to find the sum for the month, we just need to evaluate the given expression. Well, 30 divided by two is 15. Then we have two times one, which is to then we have 30 minus one, which is 29 29 times one. Well, that's still just 29. All right, well, next we have to post 29 but that's equal to 31. So we have s of 30 is equal to 15 times 31 and now we just need to multiply. Well, 15 times 31 is equal to 465 so we'll know the S of 30 is equal to 465. So what does that mean? That means the total amount deposited at the end of the month is $465. So this will be our answer

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